{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "Производная функции: 2*x\n"
          ]
        }
      ],
      "source": [
        "import sympy as sp\n",
        "\n",
        "# Определите символьные переменные\n",
        "x = sp.symbols('x')\n",
        "\n",
        "# Определите вашу функцию, например, f(x) = x^2\n",
        "f = x**2\n",
        "\n",
        "# Вычислите производную функции\n",
        "f_prime = sp.diff(f, x)\n",
        "\n",
        "# Выведите результат\n",
        "print(\"Производная функции:\", f_prime)\n",
        "\n",
        "# Этот код создает символьную переменную x, определяет функцию f(x) и затем находит ее производную, используя функцию sp.diff(). Результат выводится на экран.\n",
        "# Вы можете изменить функцию f и переменные по своему усмотрению.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 17,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "QD_IFxHoOdZm",
        "outputId": "57d90f74-18c6-48e6-91e1-4756922ee309"
      },
      "outputs": [
        {
          "name": "stdout",
          "output_type": "stream",
          "text": [
            "The derivative at x = 3 is 6.009999999999849\n"
          ]
        },
        {
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x13565c88>"
            ]
          },
          "execution_count": 17,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        " \n",
        "# Функция расчета первой производной разностным методом\n",
        "def numerical_derivative(f, x, h=1e-5):\n",
        "    return (f(x + h) - f(x)) / h\n",
        "\n",
        "# Функция расчета второй производной разностным методом\n",
        "def numerical_2nd_derivative(f, x, h=1e-5):\n",
        "    return (f(x - h) - 2 * f(x) + f(x + h)) / h ** 2\n",
        "\n",
        "# Define your function\n",
        "def f(x):\n",
        "    return x**2\n",
        "\n",
        "\n",
        "# Считаем численно первую и вторую производную функции в точке х0\n",
        "x0 = 3\n",
        "derivative_at_x = numerical_derivative(f, x0, 0.01)\n",
        "print(\"The derivative at x =\", x0, \"is\", derivative_at_x)\n",
        "h = 0.001\n",
        "x = np.linspace(-5, 5, 21)\n",
        "y = f(x)\n",
        "y1 = numerical_derivative(f, x, h)\n",
        "y2 = numerical_2nd_derivative(f, x, h)\n",
        "\n",
        "plt.plot(x,y)\n",
        "plt.scatter(x,y1)\n",
        "plt.scatter(x,y2)\n",
        "#print (y)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 21,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "djwjW54SRDeY",
        "outputId": "3ee10cd5-41aa-487a-978d-e5ddd135e121"
      },
      "outputs": [
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "H = np.linspace(1e-10, 0.1, 21)\n",
        "y1 = numerical_derivative(f, x0, H)\n",
        "\n",
        "plt.plot(H, y1, \"-o\")\n",
        "plt.show()"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 23,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 466
        },
        "id": "uhk5Y2ZhUC4S",
        "outputId": "18e071cb-0b2c-4308-bdaf-3d8c79f16b6f"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "<function print>"
            ]
          },
          "execution_count": 23,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "a = np.linspace(12, 15, 11)\n",
        "H = 10 ** (-a)\n",
        "y1 = numerical_derivative(f, x0, H)\n",
        "\n",
        "plt.plot(H,y1)\n",
        "plt.plot(H,y1, 'bs')\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "language_info": {
      "name": "python"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 2
}
